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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # What is the sum of the digits of integer x, where x = 4^10* 5^13?

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Math Expert V
Joined: 02 Sep 2009
Posts: 59712
What is the sum of the digits of integer x, where x = 4^10* 5^13?  [#permalink]

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11 00:00

Difficulty:   45% (medium)

Question Stats: 65% (01:39) correct 35% (01:42) wrong based on 205 sessions

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What is the sum of the digits of integer x, where $$x = 4^{10} * 5^{13}$$?

(A) 13

(B) 11

(C) 10

(D) 8

(E) 5

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Manager  S
Joined: 18 May 2016
Posts: 180
Location: India
GMAT 1: 710 Q48 V40 WE: Marketing (Education)
Re: What is the sum of the digits of integer x, where x = 4^10* 5^13?  [#permalink]

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X= 2^20*5^13
= 10^13 *2^7
= 128*10^13

Sum of digits = 11
Option B

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Manager  B
Joined: 06 Aug 2017
Posts: 78
GMAT 1: 570 Q50 V18 GMAT 2: 610 Q49 V24 GMAT 3: 640 Q48 V29 Re: What is the sum of the digits of integer x, where x = 4^10* 5^13?  [#permalink]

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2
Bunuel wrote:
What is the sum of the digits of integer x, where $$x = 4^{10} * 5^{13}$$?

(A) 13

(B) 11

(C) 10

(D) 8

(E) 5

$$x = 4^{10} * 5^{13} = 2^{20}*5^{13} = 10^{13}*2^7 = 10^{13}*128$$
Sum of the digits = 1+2+8 = 11

Hence B
Intern  Joined: 26 Jan 2017
Posts: 3
Re: What is the sum of the digits of integer x, where x = 4^10* 5^13?  [#permalink]

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Since we are looking for the sum of the digits we can simplify this problem by removing the trailing zeros (zeros at the end of the number). Trailing zeros are added to a number when multiplied by 10.

Remember 10 = 2 * 5
Thus, in our problem 4^10*5^13 or:
2^20 * 5^13

As you can see we have the pair 2*5 thirteen times. We can remove 2^13 and 5^13 and work with the rest which is 2^7 = 128

1+2+8 = 11
Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2809
Re: What is the sum of the digits of integer x, where x = 4^10* 5^13?  [#permalink]

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Bunuel wrote:
What is the sum of the digits of integer x, where $$x = 4^{10} * 5^{13}$$?

(A) 13

(B) 11

(C) 10

(D) 8

(E) 5

We can simplify the given equation:

x = 4^10 x 5^13

x = 2^20 x 5^13

x = 2^7 x 2^13 x 5^13

x = 2^7 x 10^13

x = 128 x 10^13

We see that x is the number 128 followed by 13 zeros. Thus, the sum of the digits of x is 1 + 2 + 8 = 11.

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# Jeffrey Miller

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Intern  S
Joined: 22 May 2018
Posts: 49
Re: What is the sum of the digits of integer x, where x = 4^10* 5^13?  [#permalink]

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1
we can use the concept of cyclicity to find out the units digit.
units digit of 4^10 is 6 and units digit of 5^13 is 5
6+5 = 11
units digit 1.
(This method works because there is no repetition of units digit in the options.)
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8680
Location: United States (CA)
Re: What is the sum of the digits of integer x, where x = 4^10* 5^13?  [#permalink]

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1
Bunuel wrote:
What is the sum of the digits of integer x, where $$x = 4^{10} * 5^{13}$$?

(A) 13

(B) 11

(C) 10

(D) 8

(E) 5

We can rewrite the expression as:

2^20 x 5^13

2^7 x 2^13 x 5^13

2^7 x 10^13

128 x 10^13

This is the number 128 followed by 13 zeros, so the sum of the digits is 1 + 2 + 8 = 11 (note: the 13 zeros will not contribute anything to the sum).

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# Scott Woodbury-Stewart

Founder and CEO

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: What is the sum of the digits of integer x, where x = 4^10* 5^13?   [#permalink] 07 Apr 2019, 19:04
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# What is the sum of the digits of integer x, where x = 4^10* 5^13?   